Single-walled carbon nanotubes grow by decomposition of a carbon-containing precursor gas over metal nanocatalysts. It is known that the shape, size, and chemical nature of the catalysts play significant roles in the nucleation and growth processes. Here, we use reactive molecular dynamics simulations to analyze how the catalyst particle size and the strength of adhesion between the surface and nascent carbon structures may affect the growth process. As a result, we determine if the process leads to cap lift-off or if it causes graphitic encapsulation and, therefore, poisoning of the catalyst. In agreement with the Hafner-Smalley model, our MD simulation results illustrate that the work of adhesion must be weak enough so the curvature energy of a spherical fullerene is less favorable than that of a single-walled carbon nanotube with the same diameter, thus allowing the cap-lifting process to take place. Moreover, we propose that a simple model combining curvature energy and kinetic effects may help to identify regions of single-walled carbon nanotube growth in the phase space defined by work of adhesion, temperature, and catalyst size.